Signal shadowing and multipath fading are two challenging phenomena in wireless communications. The goal of this thesis is to improve the statistical models and the mathematical tools required for description and analysis of some specific fading scenarios, namely lognormal shadowing, two-wave with diffuse power fading and diffuse Nakagami-m with line-of-sight fading. For lognormal shadowing, a novel method is proposed to derive approximations to the lognormal characteristic function. For two-wave with diffuse power fading, new expressions are derived for its probability density function, cumulative distribution function and moments. Finally, a novel fading model is introduced which combines a line-of-sight with a Nakagami-m diffuse scatter. The new fading model is justified and expressions are derived for its statistics. The new fading distribution is compared to the Rice, Nakagami-m and two-wave with diffuse power distributions. Application of the results in performance analysis of wireless systems operating in Nakagami-m with line-of-sight fading is investigated.

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